×

Fault-tolerant anti-synchronization control for chaotic switched neural networks with time delay and reaction diffusion. (English) Zbl 1478.93142

Summary: This paper is concerned with the issue of fault-tolerant anti-synchronization control for chaotic switched neural networks with time delay and reaction-diffusion terms under the drive-response scheme, where the response system is assumed to be disturbed by stochastic noise. Both arbitrary switching signal and average dwell-time limited switching signal are taken into account. With the aid of the Lyapunov-Krasovskii functional approach and combining with the generalized Itô formula, sufficient conditions on the mean-square exponential stability for the anti-synchronization error system are presented. Then, by utilizing some decoupling methods, constructive design strategies on the desired fault-tolerant anti-synchronization controller are proposed. Finally, an example is given to demonstrate the effectiveness of our design strategies.

MSC:

93B35 Sensitivity (robustness)
93B70 Networked control
93C20 Control/observation systems governed by partial differential equations
93C43 Delay control/observation systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] A. Abdulle; Y. Bai; G. Vilmart, Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems, Discrete Contin. Dyn. Syst. Ser. S, 8, 91-118 (2015) · Zbl 1304.65245
[2] C. K. Ahn, Adaptive \(H_{\infty}\) anti-synchronization for time-delayed chaotic neural networks, Prog. Theoretical Phys., 122, 1391-1403 (2009) · Zbl 1187.82099
[3] J. Cao; R. Rakkiyappan; K. Maheswari; A. Chandrasekar, Exponential \(H_{\infty}\) filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities, Sci. China Technol. Sci., 59, 387-402 (2016)
[4] X. Chang; R. Liu; J. H. Park, A further study on output feedback \(H_{\infty}\) control for discrete-time systems, IEEE Trans. Circuits Systems II: Express Briefs, 67, 305-309 (2020)
[5] N. D. Cong; T. S. Doan, On integral separation of bounded linear random differential equations, Discrete Contin. Dyn. Syst. Ser. S, 9, 995-1007 (2016) · Zbl 1366.37118
[6] Y. Fan; X. Huang; Y. Li; J. Xia; G. Chen, Aperiodically intermittent control for quasi-synchronization of delayed memristive neural networks: An interval matrix and matrix measure combined method, IEEE Trans. Systems Man Cybernetics: Systems, 49, 2254-2265 (2019)
[7] Y. Fan; X. Huang; H. Shen; J. Cao, Switching event-triggered control for global stabilization of delayed memristive neural networks: An exponential attenuation scheme, Neural Networks, 117, 216-224 (2019) · Zbl 1443.93079
[8] J. Fell; N. Axmacher, The role of phase synchronization in memory processes, Nature Rev. Neurosci., 12, 105-118 (2011)
[9] J. P. Hespanha and A. S. Morse, Stability of switched systems with average dwell-time, Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, AZ, 1999, 2655-2660.
[10] J. Hou; Y. Huang; S. Ren, Anti-synchronization analysis and pinning control of multi-weighted coupled neural networks with and without reaction-diffusion terms, Neurocomputing, 330, 78-93 (2019)
[11] Y.-L. Huang; S.-Y. Ren; J. Wu; B.-B. Xu, Passivity and synchronization of switched coupled reaction-diffusion neural networks with non-delayed and delayed couplings, Int. J. Comput. Math., 96, 1702-1722 (2019) · Zbl 1499.35593
[12] T. Jiao; J. H. Park; G. Zong; Y. Zhao; Q. Du, On stability analysis of random impulsive and switching neural networks, Neurocomputing, 350, 146-154 (2019)
[13] R. Konnur, Synchronization-based approach for estimating all model parameters of chaotic systems, Phys. Rev. E, 67, 1387-1396 (2003)
[14] T. H. Lee; C. P. Lim; S. Nahavandi; J. H. Park, Network-based synchronization of T-S fuzzy chaotic systems with asynchronous samplings, J. Franklin Inst., 355, 5736-5758 (2018) · Zbl 1451.93371
[15] X. Li; M. Bohner; C. K. Wang, Impulsive differential equations: Periodic solutions and applications, Automatica J. IFAC, 52, 173-178 (2015) · Zbl 1309.93074
[16] T. L. Liao; N. S. Huang, An observer-based approach for chaotic synchronization with applications to secure communications, IEEE Trans. Circuits Systems I: Fundamental Theory Appl., 46, 1144-1151 (1999) · Zbl 0963.94003
[17] Y. Liu; J. H. Park; F. Fang, Global exponential stability of delayed neural networks based on a new integral inequality, IEEE Trans. Systems Man Cybernetics: Systems, 49, 2318-2325 (2019)
[18] E. N. Lorenz, Deterministic nonperiodic flow, J. Atmospheric Sci., 20, 130-141 (1963) · Zbl 1417.37129
[19] Q. Ma; S. Xu; Y. Zou; G. Shi, Synchronization of stochastic chaotic neural networks with reaction-diffusion terms, Nonlinear Dynam., 67, 2183-2196 (2012) · Zbl 1243.93106
[20] X. Mao, Razumikhin-type theorems on exponential stability of stochastic functional differential equations, Stochastic Process. Appl., 65, 233-250 (1996) · Zbl 0889.60062
[21] S. Nakata; T. Miyata; N. Ojima; K. Yoshikawa, Self-synchronization in coupled salt-water oscillators, Phys. D, 115, 313-320 (1998) · Zbl 0962.76505
[22] N. Ozcan; M. S. Ali; J. Yogambigai; Q. Zhu; S. Arik, Robust synchronization of uncertain Markovian jump complex dynamical networks with time-varying delays and reaction-diffusion terms via sampled-data control, J. Franklin Inst., 355, 1192-1216 (2018) · Zbl 1393.93080
[23] L. M. Pecora; T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett., 64, 821-824 (1990) · Zbl 0938.37019
[24] F. Ren; J. Cao, Anti-synchronization of stochastic perturbed delayed chaotic neural networks, Neural Comput. Appl., 18, 515-521 (2009)
[25] I. Stamova; T. Stamov; X. Li, Global exponential stability of a class of impulsive cellular neural networks with supremums, Internat. J. Adapt. Control Signal Process., 28, 1227-1239 (2014) · Zbl 1338.93316
[26] V. Sundarapandian; R. Karthikeyan, Anti-synchronization of Lü and Pan chaotic systems by adaptive nonlinear control, European J. Sci. Res., 64, 94-106 (2011)
[27] W. Tai; Q. Teng; Y. Zhou; J. Zhou; Z. Wang, Chaos synchronization of stochastic reaction-diffusion time-delay neural networks via non-fragile output-feedback control, Appl. Math. Comput., 354, 115-127 (2019) · Zbl 1428.93092
[28] Z. Wang; L. Li; Y. Li; Z. Cheng, Stability and Hopf bifurcation of a three-neuron network with multiple discrete and distributed delays, Neural Process. Lett., 48, 1481-1502 (2018)
[29] I. Wedekind and U. Parlitz, Synchronization and antisynchronization of chaotic power drop-outs and jump-ups of coupled semiconductor lasers, Phys. Rev. E, 66 (2002).
[30] J. Xia; G. Chen; W. Sun, Extended dissipative analysis of generalized Markovian switching neural networks with two delay components, Neurocomputing, 260, 275-283 (2017)
[31] Z. Yan, X. Huang and J. Cao, Variable-sampling-period dependent global stabilization of delayed memristive neural networks via refined switching event-triggered control, SCIENCE CHINA Information Sciences, in progress.
[32] D. Ye; G. Yang, Adaptive fault-tolerant tracking control against actuator faults with application to flight control, IEEE Trans. Control Systems Tech, 14, 1088-1096 (2006)
[33] E. Yucel; M. S. Ali; N. Gunasekaran; S. Arik, Sampled-data filtering of Takagi-Sugeno fuzzy neural networks with interval time-varying delays, Fuzzy Sets and Systems, 316, 69-81 (2017) · Zbl 1392.93031
[34] X. Zhang; X. Lv; X. Li, Sampled-data-based lag synchronization of chaotic delayed neural networks with impulsive control, Nonlinear Dynam., 90, 2199-2207 (2017) · Zbl 1380.34082
[35] W. Zhang; S. Yang; C. Li; Z. Li, Finite-time and fixed-time synchronization of complex networks with discontinuous nodes via quantized control, Neural Process. Lett., 50, 2073-2086 (2019)
[36] D. Zhang; L. Yu; Q. G. Wang; C. J. Ong, Estimator design for discrete-time switched neural networks with asynchronous switching and time-varying delay, IEEE Trans. Neural Networks Learning Systems, 23, 827-834 (2012)
[37] J. Zhou; Y. Wang; X. Zheng; Z. Wang; H. Shen, Weighted \(H_{\infty}\) consensus design for stochastic multi-agent systems subject to external disturbances and ADT switching topologies, Nonlinear Dyn., 96, 853-868 (2019) · Zbl 1437.93126
[38] Y. Zhou; J. Xia; H. Shen; J. Zhou; Z. Wang, Extended dissipative learning of time-delay recurrent neural networks, J. Franklin Inst., 356, 8745-8769 (2019) · Zbl 1423.93119
[39] J. Zhou; S. Xu; H. Shen; B. Zhang, Passivity analysis for uncertain BAM neural networks with time delays and reaction-diffusions, Internat. J. Systems Sci., 44, 1494-1503 (2013) · Zbl 1277.93034
[40] K. Zhou; P. P. Khargonekar, Robust stabilization of linear systems with norm-bounded time-varying uncertainty, Systems Control Lett., 10, 17-20 (1988) · Zbl 0634.93066
[41] J. Zhou; J. H. Park; Q. Ma, Non-fragile observer-based \(H_{\infty}\) control for stochastic time-delay systems, Appl. Math. Comput., 291, 69-83 (2016) · Zbl 1410.93117
[42] G. Zhuang; Q. Ma; B. Zhang; S. Xu; J. Xia, Admissibility and stabilization of stochastic singular Markovian jump systems with time delays, Systems Control Lett., 114, 1-10 (2018) · Zbl 1388.93104
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.